Finite Group Databasebeta

← #30550750

Subgroups — #30550750

Order 15616.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519751C211yesmaximal, characteristic, complemented
2#21456629C214yesmaximal, complemented
3#21456621C212yesmaximal, complemented
4#21456616C212yesmaximal, complemented
5#21456580C214yesmaximal, complemented
6#21456572C212yesmaximal, complemented
7#21456567C212yesmaximal, complemented
8#21455759C212yesmaximal, complemented
9#21455739C212yesmaximal, complemented
10#21455440C214yesmaximal, complemented
11#21455071C212yesmaximal, complemented
12#21455045C212yesmaximal, complemented
13C2×#16839726C211yesmaximal, characteristic, complemented
14C2×C61×#525C211yesmaximal, characteristic, complemented
15C23×D244C2211yescharacteristic, complemented
16C23×C22⋊D61—21no—
17C2×#14519802C2214yescomplemented
18C22×#11758194C2212yescomplemented
19C2×#14519751—21no—
20C2×#14519751—21no—
21C2×#14519751—21no—
22C2×#14519751—21no—
23C2×#14519751—21no—
24C2×#14519751—21no—
25C2×#14519751C2212yes—
26C2×#14519751C2212yes—
27C2×#14519751C2212yes—
28C2×#14519751C2212yescomplemented
29C2×#14519751C2212yescomplemented
30C2×#14519751C2212yescomplemented
31C22×C4⋊Dic61C2211yescharacteristic, complemented
32C22×#11758198—21no—
33#16840095C2214yescomplemented
34#16840090C2214yescomplemented
35#16840086C2218yescomplemented
36#16840080C2214yescomplemented
37#16840078C2214yescomplemented
38#16840075C2214yescomplemented
39#16840073C2214yescomplemented
40#16840013C2218yescomplemented
41#16840010C2218yescomplemented
42#16839996C2218yescomplemented
43#16839993C2218yescomplemented
44#16839912C2214yescomplemented
45#16839912C2214yescomplemented
46#16839907C2218yescomplemented
47#16839901C2214yescomplemented
48#16839896C2214yescomplemented
49#16839895C2214yescomplemented
50#16839895C2214yescomplemented
51#16839805C2214yescomplemented
52#16839766C2214yescomplemented
53#16839763C2214yescomplemented
54#16839726C2212yescomplemented
55#16839726C2212yescomplemented
56#16839726C2212yescomplemented
57#16839726C2212yescomplemented
58C2×C22⋊#92418C2212yescomplemented
59C2×C22⋊#92418C2212yescomplemented
60C22×#41×C61C2211yescharacteristic, complemented
61C24×C4×C61C2211yescharacteristic
62C61×#525—21no—
63C61×#525—21no—
64C61×#525—21no—
65C61×#525—21no—
66C61×#525C2212yes—
67C61×#525C2212yescomplemented
68C61×#525C2212yescomplemented
69C61×#525C2212yescomplemented
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic, complemented
72C2×C22⋊Q8×C61C2211yescharacteristic, complemented
73C2×#121×C61C2211yescharacteristic, complemented
74C2×#121×C61C2211yescharacteristic, complemented
75C2×#120×C61—21no—
76C2×C4×D4×C61—21no—
77C2×C4×D4×C61—21no—
78C2×#117×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244—44no—
84C22×D244C2312yes—
85C22×D244C2312yes—
86C22×D244C2312yes—
87C22×C22⋊D61—22no—
88C22×C22⋊D61—22no—
89C22×C22⋊D61—22no—
90C22×C22⋊D61—22no—
91C22×C22⋊D61—22no—
92C22×C22⋊D61—22no—
93C22×C22⋊D61—48no—
94C23×Dic61—21no—
95#14519802—48no—
96C2×#11758201C2318yescomplemented
97C2×#11758199C2318yescomplemented
98C2×#11758194—44no—
99C2×#11758194C2314yes—
100C2×#11758194C2314yescomplemented
101C22×#92418C2314yescomplemented
102#14519751—22no—
103#14519751—22no—
104#14519751—22no—
105#14519751—22no—
106#14519751—22no—
107#14519751—22no—
108#14519751—22no—
109#14519751—22no—
110#14519751—22no—
111#14519751—22no—
112#14519751—22no—
113#14519751—22no—
114#14519751C2314yes—
115#14519751C2314yes—
116#14519751C2314yes—
117#14519751C2314yes—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2312yes—
122C2×C4⋊Dic61C2312yes—
123C2×C4⋊Dic61C2312yes—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130#14519710C2318yescomplemented
131#14519708C2318yescomplemented
132#14519701C2318yescomplemented
133#14519698C2318yescomplemented
134#14519697C2318yescomplemented
135#14519697C2318yescomplemented
136C22⋊#92418C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yescomplemented
139C22⋊#92418C2314yescomplemented
140C25×C61D411yescharacteristic
141C2×#41×C61—21no—
142C2×#41×C61—21no—
143C2×#41×C61—44no—
144C2×#41×C61C2312yes—
145C2×#41×C61C2312yescomplemented
146C22×Q8×C61C2311yescharacteristic, complemented
147C22×D4×C61—21no—
148C22×D4×C61—21no—
149C22×D4×C61—21no—
150C22×D4×C61C2311yescharacteristic, complemented
151C23×C4×C61—21no—
152C23×C4×C61—44no—
153C23×C4×C61D411yescharacteristic
154C23×C4×C61D411yescharacteristic
155C23×C4×C61D411yescharacteristic
156C23×C4×C61D411yescharacteristic
157C23×C4×C61D411yescharacteristic
158C23×C4×C61D411yescharacteristic
159C23×C4×C61D411yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167#123×C61—22no—
168#123×C61—22no—
169#123×C61—22no—
170#123×C61—22no—
171C22⋊Q8×C61—21no—
172C22⋊Q8×C61—21no—
173C22⋊Q8×C61—21no—
174C22⋊Q8×C61—21no—
175C22⋊Q8×C61C2312yes—
176C22⋊Q8×C61C2312yes—
177C22⋊Q8×C61C2312yescomplemented
178C22⋊Q8×C61C2312yescomplemented
179#121×C61—21no—
180#121×C61—21no—
181#121×C61—21no—
182#121×C61—21no—
183#121×C61C2312yes—
184#121×C61C2312yes—
185#121×C61C2312yescomplemented
186#121×C61C2312yescomplemented
187#120×C61—22no—
188#120×C61—22no—
189#120×C61—22no—
190#120×C61—22no—
191C4×D4×C61—22no—
192C4×D4×C61—22no—
193C4×D4×C61—22no—
194C4×D4×C61—22no—
195C4×D4×C61—22no—
196C4×D4×C61—22no—
197C4×D4×C61—22no—
198C4×D4×C61—22no—
199#117×C61—21no—
200#117×C61—21no—
201#117×C61C2312yes—
202#117×C61C2312yescomplemented
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61—21no—
205C2×C4⋊C4×C61C2311yescharacteristic, complemented
206C2×C4⋊C4×C61C2311yescharacteristic, complemented
207C2×C22⋊C4×C61—21no—
208C2×C22⋊C4×C61—21no—
209C2×C22⋊C4×C61—21no—
210C2×C22⋊C4×C61—21no—
211C2×C22⋊C4×C61—21no—
212C2×C42×C61—21no—
213C24×C61—24no—
214C24×C61—21no—
215C24×C61—42no—
216C24×C61—42no—
217C24×C61C2×D411yescharacteristic
218C24×C61C2×D411yescharacteristic
219C24×C61C2×D411yescharacteristic
220C24×C61C2×D411yescharacteristic
221C24×C61C2×D411yescharacteristic
222C24×C61C2×D411yescharacteristic
223C24×C61C2×D411yescharacteristic
224C23×D61—22no—
225C23×D61—22no—
226C23×D61—22no—
227C23×D61—44no—
228C23×D61—44no—
229C23×D61—44no—
230#41×C61—28no—
231#41×C61—44no—
232#41×C61—44no—
233#41×C61—44no—
234C2×Q8×C61—21no—
235C2×Q8×C61—42no—
236C2×Q8×C61C2412yes—
237C2×D4×C61—22no—
238C2×D4×C61—22no—
239C2×D4×C61—22no—
240C2×D4×C61—22no—
241C2×D4×C61—22no—
242C2×D4×C61—22no—
243C2×D4×C61—21no—
244C2×D4×C61—42no—
245C2×D4×C61—44no—
246C2×D4×C61—44no—
247C2×D4×C61—44no—
248C2×D4×C61C2412yes—
249C22×C4×C61—24no—
250C22×C4×C61—24no—
251C22×C4×C61—24no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—22no—
256C22×C4×C61—22no—
257C22×C4×C61—42no—
258C22×C4×C61—42no—
259C22×C4×C61—42no—
260C22×C4×C61—42no—
261C22×C4×C61—42no—
262C22×C4×C61—42no—
263C22×C4×C61—42no—
264C22×C4×C61—42no—
265C22×C4×C61—42no—
266C22×C4×C61—42no—
267C22×C4×C61—42no—
268C22×C4×C61—44no—
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D411yescharacteristic
282C22×C4×C61C2×D411yescharacteristic
283C22×C4×C61C2×D411yescharacteristic
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291C22×C4×C61C2411yescharacteristic
292C22×C4×C61C2411yescharacteristic
293C22×C4×C61C2411yescharacteristic
294C22×C4×C61C2411yescharacteristic
295C22×C4×C61C2411yescharacteristic
296C22×C4×C61C2411yescharacteristic
297C2×C22⋊D61—24no—
298C2×C22⋊D61—24no—
299C2×C22⋊D61—24no—
300C2×C22⋊D61—24no—
301C2×C22⋊D61—48no—
302C2×C22⋊D61—48no—
303C2×C22⋊D61—48no—
304C2×C22⋊D61—48no—
305C2×C22⋊D61—48no—
306C2×C22⋊D61—48no—
307C22×Dic61—22no—
308C22×Dic61—22no—
309C22×Dic61—22no—
310C22×Dic61—44no—
311C2×D244—28no—
312C2×D244—22no—
313C2×D244—22no—
314C2×D244—22no—
315C2×D244—44no—
316C2×D244—44no—
317C2×D244—44no—
318C2×D244—44no—
319C2×D244—44no—
320C2×D244C2414yes—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61—22no—
325C4⋊C4×C61—21no—
326C4⋊C4×C61—21no—
327C4⋊C4×C61C2412yes—
328C4⋊C4×C61C2412yes—
329C22⋊C4×C61—22no—
330C22⋊C4×C61—22no—
331C22⋊C4×C61—22no—
332C22⋊C4×C61—22no—
333C22⋊C4×C61—22no—
334C22⋊C4×C61—22no—
335C22⋊C4×C61—22no—
336C22⋊C4×C61—22no—
337C22⋊C4×C61—22no—
338C22⋊C4×C61—22no—
339C42×C61—22no—
340C42×C61—22no—
341#11758201—48no—
342#11758199—48no—
343#11758198—24no—
344#11758198—24no—
345#11758198—24no—
346#11758198—24no—
347C4⋊Dic61—22no—
348C4⋊Dic61—22no—
349C4⋊Dic61—22no—
350C4⋊Dic61C2414yes—
351#11758194—28no—
352#11758194—44no—
353C2×#92418—44no—
354C2×#92418C2418yes—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—416no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—42no—
380C23×C61AGL(1,ℤ/8)14yescomplemented
381C23×C61C22×D411yescharacteristic
382C23×C61C22×D411yescharacteristic
383C23×C61C22×D411yescharacteristic
384C23×C61C22×D411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C22×D61—24no—
389C22×D61—44no—
390C22×D61—44no—
391C22×D61—44no—
392C22×D61—44no—
393C22×D61—44no—
394C22×D61—44no—
395C22×D61—44no—
396C22×D61—44no—
397C22×D61—44no—
398C22×D61—816no—
399Q8×C61—24no—
400Q8×C61—42no—
401D4×C61—24no—
402D4×C61—42no—
403D4×C61—44no—
404D4×C61—44no—
405D4×C61—44no—
406D4×C61—44no—
407D4×C61—44no—
408D4×C61—44no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—44no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61—44no—
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61C22×D411yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C22×D411yescharacteristic
448C2×C4×C61C22×D411yescharacteristic
449C2×C4×C61C22×D411yescharacteristic
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61H(5,𝔽2)14yes—
452C2×C4×C61C2511yescharacteristic
453C22⋊D61—48no—
454C22⋊D61—48no—
455C22⋊D61—48no—
456C22⋊D61—48no—
457C2×Dic61—24no—
458C2×Dic61—44no—
459C2×Dic61—44no—
460C2×Dic61—44no—
461D244—28no—
462D244—44no—
463D244—44no—
464D244—44no—
465#92418—28no—
466#60750—611nomaximal, Sylow
467C22×C61—28no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—44no—
485C22×C61—44no—
486C22×C61—44no—
487C22×C61—44no—
488C22×C61—44no—
489C22×C61—44no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—84no—
494C22×C61#53412yes—
495C22×C61C2×AGL(1,ℤ/8)12yes—
496C22×C61C2×AGL(1,ℤ/8)12yes—
497C22×C61C2×AGL(1,ℤ/8)12yes—
498C22×C61#57512yes—
499C22×C61C23×D411yescharacteristic
500C2×D61—44no—
501C2×D61—44no—
502C2×D61—44no—
503C2×D61—88no—
504C2×D61—88no—
505C2×D61—88no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—42no—
513C4×C61—42no—
514C4×C61—42no—
515C4×C61#53412yes—
516C4×C61C2×H(5,𝔽2)12yes—
517Dic61—44no—
518C2×#525D6111yescharacteristic, complemented
519C22×#121—611no—
520#3194—614no—
521#3193—612no—
522#3192—612no—
523#3188—614no—
524#3187—612no—
525#3186—612no—
526#3094—612no—
527#3092—612no—
528#3055—614no—
529#3006—612no—
530#3003—612no—
531C2×#407—611no—
532C2×C61—22no—
533C2×C61—22no—
534C2×C61—22no—
535C2×C61—22no—
536C2×C61—22no—
537C2×C61—41no—
538C2×C61—41no—
539C2×C61—82no—
540C2×C61C2×#53411yescharacteristic
541C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C61C2×#57511yescharacteristic
543D61—84no—
544C22×#41C2×D6111yescharacteristic, complemented
545C23×D4—611no—
546C23×D4—1221no—
547C24×C4C2×D6111yescharacteristic
548C2×AGL(1,ℤ/8)—614no—
549C22×M16—612no—
550#525—21no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525C2×D6112yes—
555#525C2×D6112yescomplemented
556#525C2×D6112yescomplemented
557#525C2×D6112yescomplemented
558C2×#123—21no—
559C2×C22⋊Q8C2×D6111yescharacteristic, complemented
560C2×C22⋊Q8C2×D6111yescharacteristic, complemented
561C2×#121—612no—
562C2×#121—612no—
563C2×#121—612no—
564C2×#121—612no—
565C2×#121—612no—
566C2×#121—612no—
567C2×#121—1221no—
568C2×#121—1221no—
569C2×#121—1221no—
570C2×#121—1221no—
571C2×#121—1221no—
572C2×#121—1221no—
573C2×#121C2×D6111yescharacteristic, complemented
574C2×#121C2×D6111yescharacteristic, complemented
575C2×#120—21no—
576C2×C4×D4—21no—
577C2×C4×D4—21no—
578C2×#117C2×D6111yescharacteristic, complemented
579C22×C4⋊C4—611no—
580C22×C22⋊C4—1221no—
581#484—614no—
582#483—614no—
583#482—618no—
584#481—614no—
585#481—614no—
586#480—614no—
587#480—614no—
588#469—618no—
589#468—618no—
590#466—618no—
591#465—618no—
592#450—614no—
593#450—614no—
594#449—618no—
595#448—614no—
596#447—614no—
597#447—614no—
598#447—614no—
599#428—614no—
600#418—614no—
601#417—614no—
602#407—612no—
603#407—612no—
604#407—612no—
605#407—612no—
606C2×C22⋊C8—612no—
607C2×C22⋊C8—612no—
608C61#6075011yescharacteristic, complemented, Sylow
609C25—1221no—
610C25C22⋊D6111yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D6112yes—
615C2×#41C22×D6112yescomplemented
616C22×Q8C22×D6111yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—612no—
621C22×D4—612no—
622C22×D4—612no—
623C22×D4—1222no—
624C22×D4—1222no—
625C22×D4—1222no—
626C22×D4—1222no—
627C22×D4—1222no—
628C22×D4—1222no—
629C22×D4—1221no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4—2444no—
633C22×D4—2448no—
634C22×D4C22×D6111yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1221no—
638C23×C4C22⋊D6111yescharacteristic
639C23×C4C22⋊D6111yescharacteristic
640C23×C4C22⋊D6111yescharacteristic
641C23×C4C22⋊D6111yescharacteristic
642C23×C4C22⋊D6111yescharacteristic
643C23×C4C22⋊D6111yescharacteristic
644C23×C4C22⋊D6111yescharacteristic
645C23×C4C22×D6111yescharacteristic
646C23×C4C22×D6111yescharacteristic
647C23×C4C22×D6111yescharacteristic
648C23×C4C22×D6111yescharacteristic
649C23×C4C22×D6111yescharacteristic
650C23×C4C22×D6111yescharacteristic
651C23×C4C22×D6111yescharacteristic
652AGL(1,ℤ/8)—2448no—
653C2×SD16—618no—
654C2×D8—618no—
655C2×M16—614no—
656C2×M16—614no—
657C2×M16—2444no—
658C22×C8—614no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D6112yes—
668C22⋊Q8C22×D6112yes—
669C22⋊Q8C22×D6112yescomplemented
670C22⋊Q8C22×D6112yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—614no—
676#121—614no—
677#121—614no—
678#121—614no—
679#121—1222no—
680#121—1222no—
681#121—1222no—
682#121—1222no—
683#121—1222no—
684#121—1222no—
685#121—1222no—
686#121—1222no—
687#121—1222no—
688#121—1222no—
689#121—1222no—
690#121—1222no—
691#121C22×D6112yes—
692#121C22×D6112yes—
693#121C22×D6112yescomplemented
694#121C22×D6112yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D6112yes—
710#117C22×D6112yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—612no—
714C2×C4⋊C4—612no—
715C2×C4⋊C4—612no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4C22×D6111yescharacteristic, complemented
720C2×C4⋊C4C22×D6111yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C42—21no—
733#107—618no—
734#106—618no—
735#103—618no—
736#102—618no—
737#102—618no—
738#102—618no—
739C22⋊C8—614no—
740C22⋊C8—614no—
741C22⋊C8—614no—
742C22⋊C8—614no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—1222no—
748C24—1222no—
749C24—1222no—
750C24—2444no—
751C24—2444no—
752C24—2444no—
753C24C2×C22⋊D6111yescharacteristic
754C24C2×C22⋊D6111yescharacteristic
755C24C2×C22⋊D6111yescharacteristic
756C24C2×C22⋊D6111yescharacteristic
757C24C2×C22⋊D6111yescharacteristic
758C24C2×C22⋊D6111yescharacteristic
759C24C2×C22⋊D6111yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D6112yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—614no—
779C2×D4—1224no—
780C2×D4—1224no—
781C2×D4—1224no—
782C2×D4—1224no—
783C2×D4—1222no—
784C2×D4—1222no—
785C2×D4—1222no—
786C2×D4—1228no—
787C2×D4—2444no—
788C2×D4—2444no—
789C2×D4—2444no—
790C2×D4—2444no—
791C2×D4—2444no—
792C2×D4—2448no—
793C2×D4—2448no—
794C2×D4—2448no—
795C2×D4—2448no—
796C2×D4—2448no—
797C2×D4—2448no—
798C2×D4C23×D6112yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—1222no—
822C22×C4—2444no—
823C22×C4C2×C22⋊D6111yescharacteristic
824C22×C4C2×C22⋊D6111yescharacteristic
825C22×C4C2×C22⋊D6111yescharacteristic
826C22×C4C2×C22⋊D6111yescharacteristic
827C22×C4C2×C22⋊D6111yescharacteristic
828C22×C4C2×C22⋊D6111yescharacteristic
829C22×C4C2×C22⋊D6111yescharacteristic
830C22×C4C2×C22⋊D6111yescharacteristic
831C22×C4C2×C22⋊D6111yescharacteristic
832C22×C4C2×C22⋊D6111yescharacteristic
833C22×C4C2×C22⋊D6111yescharacteristic
834C22×C4C2×C22⋊D6111yescharacteristic
835C22×C4C2×C22⋊D6111yescharacteristic
836C22×C4C2×C22⋊D6111yescharacteristic
837C22×C4C2×C22⋊D6111yescharacteristic
838C22×C4C2×C22⋊D6111yescharacteristic
839C22×C4C2×C22⋊D6111yescharacteristic
840C22×C4C2×C22⋊D6111yescharacteristic
841C22×C4C2×C22⋊D6111yescharacteristic
842C22×C4C2×C22⋊D6111yescharacteristic
843C22×C4C2×C22⋊D6111yescharacteristic
844C22×C4C23×D6111yescharacteristic
845C22×C4C23×D6111yescharacteristic
846C22×C4C23×D6111yescharacteristic
847C22×C4C23×D6111yescharacteristic
848C22×C4C23×D6111yescharacteristic
849C22×C4C23×D6111yescharacteristic
850C22×C4C23×D6111yescharacteristic
851SD16—2448no—
852D8—2448no—
853M16—1228no—
854M16—2444no—
855C2×C8—618no—
856C2×C8—2444no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—614no—
864C4⋊C4—1222no—
865C4⋊C4—1222no—
866C4⋊C4—1222no—
867C4⋊C4C23×D6112yes—
868C4⋊C4C23×D6112yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1224no—
880C22⋊C4—1224no—
881C22⋊C4—1224no—
882C22⋊C4—1224no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—1224no—
911C23—48816no—
912C23—2444no—
913C23—2444no—
914C23—2444no—
915C23—2444no—
916C23—2444no—
917C23—2444no—
918C23—2444no—
919C23—2444no—
920C23—2444no—
921C23#1451980214yescomplemented
922C23C22×C22⋊D6111yescharacteristic
923C23C22×C22⋊D6111yescharacteristic
924C23C22×C22⋊D6111yescharacteristic
925C23C22×C22⋊D6111yescharacteristic
926C23C22×C22⋊D6111yescharacteristic
927C23C22×C22⋊D6111yescharacteristic
928C23C22×C22⋊D6111yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—1228no—
940D4—2444no—
941D4—2444no—
942D4—2448no—
943D4—2448no—
944D4—2448no—
945D4—2448no—
946D4—2444no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—1224no—
983C2×C4—2444no—
984C2×C4—2444no—
985C2×C4—2444no—
986C2×C4C22×C22⋊D6111yescharacteristic
987C2×C4C22×C22⋊D6111yescharacteristic
988C2×C4C22×C22⋊D6111yescharacteristic
989C2×C4C22×C22⋊D6111yescharacteristic
990C2×C4C22×C22⋊D6111yescharacteristic
991C2×C4C22×C22⋊D6111yescharacteristic
992C2×C4C22×C22⋊D6111yescharacteristic
993C2×C4#1451982214yes—
994C2×C4C24×D6111yescharacteristic
995C8—1228no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—4888no—
1024C22—4888no—
1025C22—4888no—
1026C22—2444no—
1027C22—2444no—
1028C22—2444no—
1029C22#1684032112yes—
1030C22C2×#1451980212yes—
1031C22C2×#1451980212yes—
1032C22C2×#1451980212yes—
1033C22#1684056012yes—
1034C22C23×C22⋊D6111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—2444no—
1045C4#1684032112yes—
1046C4C2×#1451982212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—4884no—
1056C2C2×#1684032111yescharacteristic
1057C2C22×#1451980211yescharacteristic
1058C2C2×#1684056011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#525C2
socleC22×C61C23×D4
hypercenterC2×#525D61
hypocenterC61#60750
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14519751C2semidirect
2. #21456629C2semidirect
3. #21456621C2semidirect
4. #21456616C2semidirect
5. #21456580C2semidirect
6. #21456572C2semidirect
7. #21456567C2semidirect
8. #21455759C2semidirect
9. #21455739C2semidirect
10. #21455440C2semidirect
11. #21455071C2semidirect
12. #21455045C2semidirect
13. C2×#16839726C2semidirect
14. C2×C61×#525C2semidirect
15. C23×D244C22semidirect
17. C2×#14519802C22semidirect
18. C22×#11758194C22semidirect
28. C2×#14519751C22semidirect
29. C2×#14519751C22semidirect
30. C2×#14519751C22semidirect
31. C22×C4⋊Dic61C22semidirect
33. #16840095C22semidirect
34. #16840090C22semidirect
35. #16840086C22semidirect
36. #16840080C22semidirect
37. #16840078C22semidirect
38. #16840075C22semidirect
39. #16840073C22semidirect
40. #16840013C22semidirect
41. #16840010C22semidirect
42. #16839996C22semidirect
43. #16839993C22semidirect
44. #16839912C22semidirect
45. #16839912C22semidirect
46. #16839907C22semidirect
47. #16839901C22semidirect
48. #16839896C22semidirect
49. #16839895C22semidirect
50. #16839895C22semidirect
51. #16839805C22semidirect
52. #16839766C22semidirect
53. #16839763C22semidirect
54. #16839726C22semidirect
55. #16839726C22semidirect
56. #16839726C22semidirect
57. #16839726C22semidirect
58. C2×C22⋊#92418C22semidirect
59. C2×C22⋊#92418C22semidirect
60. C22×#41×C61C22semidirect
67. C61×#525C22semidirect
68. C61×#525C22semidirect
69. C61×#525C22semidirect
71. C2×C22⋊Q8×C61C22semidirect
72. C2×C22⋊Q8×C61C22semidirect
73. C2×#121×C61C22semidirect
74. C2×#121×C61C22semidirect
78. C2×#117×C61C22semidirect
96. C2×#11758201C23semidirect
97. C2×#11758199C23semidirect
100. C2×#11758194C23semidirect
101. C22×#92418C23semidirect
130. #14519710C23semidirect
131. #14519708C23semidirect
132. #14519701C23semidirect
133. #14519698C23semidirect
134. #14519697C23semidirect
135. #14519697C23semidirect
138. C22⋊#92418C23semidirect
139. C22⋊#92418C23semidirect
145. C2×#41×C61C23semidirect
146. C22×Q8×C61C23semidirect
150. C22×D4×C61C23semidirect
177. C22⋊Q8×C61C23semidirect
178. C22⋊Q8×C61C23semidirect
185. #121×C61C23semidirect
186. #121×C61C23semidirect
202. #117×C61C23semidirect
205. C2×C4⋊C4×C61C23semidirect
206. C2×C4⋊C4×C61C23semidirect
380. C23×C61AGL(1,ℤ/8)semidirect
518. C2×#525D61semidirect
544. C22×#41C2×D61semidirect
555. #525C2×D61semidirect
556. #525C2×D61semidirect
557. #525C2×D61semidirect
559. C2×C22⋊Q8C2×D61semidirect
560. C2×C22⋊Q8C2×D61semidirect
573. C2×#121C2×D61semidirect
574. C2×#121C2×D61semidirect
578. C2×#117C2×D61semidirect
608. C61#60750semidirect
615. C2×#41C22×D61semidirect
616. C22×Q8C22×D61semidirect
634. C22×D4C22×D61semidirect
669. C22⋊Q8C22×D61semidirect
670. C22⋊Q8C22×D61semidirect
693. #121C22×D61semidirect
694. #121C22×D61semidirect
710. #117C22×D61semidirect
719. C2×C4⋊C4C22×D61semidirect
720. C2×C4⋊C4C22×D61semidirect
921. C23#14519802semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145197512
#214566292
#214566212
#214566162
#214565802
#214565722
#214565672
#214557592
#214557392
#214554402
#214550712
#214550452
C2×#168397262
C2×C61×#5252
#6075061